# Math Help - Harry's Discount

1. ## Harry's Discount

Hi,

I need the reasoning behind the answer for this question explained, please.

At Harry’s Discount Hardware everything is sold for 20% less than the price marked. If Harry buys tool kits for $80, what price should he mark them if he wants to make a 20% profit on his cost? The answer given is$120.

My reasoning was to find 20% of 80 then subtract it from 80, then add it back and the answer would be 80. Upon recognizing the abject failure of this attempt I reasoned it another way: he wants to make a 20% profit and the discount for everything would be 20%, so I found 40% of 80, 32, and added it to 80. The answer equaling $112. I used 40% because splitting it in half gives 20 a piece. One of the 20%'s is the profit and the other is the discount. In truth my understanding of the question is a little murky and my reasoning skills are unenviable. 2. Okay, the problem with percentages is, that you can't just "split them in half". Percentages are relative to something. In this case, the 20% discount is relative to the pricetag, while the 20% profit is relative to the$80 Harry buys toolkits for.

So, he wants to make 20% profit.
This means he wants to receive 0.20*80+80=$96 This does not yet include the discount. Then he wants to price it as such, that once the discount is calculated, what is left over is$96.
This means $96 is equal to 80% (100%-20%) Therefore you need to solve 0.80*x=$96, and x is the price that goes on the price tag.

Does this make it clear?

3. I get the first part. Though I wonder if the discount could have been found first.

Originally Posted by Pim
This means $96 is equal to 80% (100%-20%) Therefore you need to solve 0.80*x=$96, and x is the price that goes on the price tag.

Does this make it clear?
I'm not understanding this part. Why did you subtract 20% from 100%? I'm not entirely sure how you arrived at the equation. Division seems a good choice but I don't understand why. I multiplied 96 by 0.80, result never made sense. Added 20% of 80 to 96, 112, made sense (only because 112 is an answer option). Essentially I'm just guessing.

4. So, my reasoning was the following:

You have the pricetag that Harry puts on the tool kit. Let's call this price "x". Now, a customer walks in, and he sees the sign "Everything 20% off". Therefore if he sees a pricetag of $100, he expects to pay$80. (This is how percentages are relative.)
Now, the customer sees the price tag of "x". x must be chosen as such that he expects to pay $96. (This way Harry makes his 20% profit.) Therefore, the price x, can be split in two parts: 80% is the price he actually pays ($96), 20% is the discount.

Normally, if you calculate a percentage of something, you can multiply by the percentage divided by hundred. Therefore, the price (x) multiplied by 80/100 (0.8) should be equal to $96 I don't know how much experience you have with solving equations. So, I'm going to teach you a relatively simple, but un-mathematical trick. So, you know 0.80*x=$96
You can compare this to 2*3=6
You know that 3 = 6/2
Therefore, x = $96/0.80 =$120

I hope this answers your question, if not, don't hesitate to ask about anything that's unclear.

5. Yeah, I feel more comfortable with it now. Thank you.